• Corpus ID: 249282197

Haagerup's phase transition at polydisc slicing

  title={Haagerup's phase transition at polydisc slicing},
  author={Giorgos Chasapis and Salil Singh and Tomasz Tkocz},
. We establish a sharp comparison inequality between the negative moments and the second moment of the magnitude of sums of independent random vectors uniform on three-dimensional Euclidean spheres. This provides a probabilistic extension of the Oleszkiewicz-Pe lczy´nski polydisc slicing result. The Haagerup-type phase transition occurs exactly when the p -norm recovers volume, in contrast to the real case. We also obtain partial results in higher dimensions. 

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